Site-wide operations management optimization for manufacturing and processing control

ABSTRACT

Aspects of the invention include implemented method includes selecting an optimization algorithm for the control system of a processing plant based on whether the control system is guided by a linear-based predictive model or a non-linear-based predictive model, in which a gradient is available. Calculating set-point variables using the optimization algorithm. Predicting an output based on the calculated set-point variables. Comparing an actual output at the processing plant to the predicted output. Suspending a physical process at the processing plant in response to the actual output being a threshold value apart from the predicted output.

BACKGROUND

The present invention generally relates to programmable computingdevices, and more specifically, to computing devices,computer-implemented methods, and computer program products configuredto optimize operations management for manufacturing and processingcontrol.

Large scale manufacturing and processing facilities use complexcomputer-based control systems to regulate the sub-processes and overallprocesses used to produce goods. A control system is a set of electronicand mechanical devices that monitor real-time data and regulate eachsub-process of the production process. The control systems control theoutput of one sub-process to be an optimal input of one or more ensuingsub-processes. Sensors perform real-time monitoring of each input,sub-process mechanism, and output and provide the data to the controlsystem. The control system monitors the sensor data and can causesmodifications to the input or mechanisms if there is an issue with theoutput.

SUMMARY

Embodiments of the present invention are directed to a site-wideoperations management optimization for manufacturing and processcontrol. A non-limiting example computer-implemented method includesselecting an optimization algorithm for the control system of aprocessing plant based on whether the control system is guided by alinear-based predictive model or a non-linear-based predictive model, inwhich a gradient is available. Calculating a set variable using theoptimization algorithm. Predicting an output based on the calculated setvariable. Comparing an actual output at the processing plant to thepredicted output. Suspending a physical process at the processing plantin response to the actual output being a threshold value apart from thepredicted output.

Other embodiments of the present invention implement features of theabove-described method in computer systems and computer programproducts.

Additional technical features and benefits are realized through thetechniques of the present invention. Embodiments and aspects of theinvention are described in detail herein and are considered a part ofthe claimed subject matter. For a better understanding, refer to thedetailed description and to the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The specifics of the exclusive rights described herein are particularlypointed out and distinctly claimed in the claims at the conclusion ofthe specification. The foregoing and other features and advantages ofthe embodiments of the invention are apparent from the followingdetailed description taken in conjunction with the accompanying drawingsin which:

FIG. 1 illustrates a block diagram of components of a manufacturing andprocess control system in accordance with one or more embodiments of thepresent invention;

FIG. 2 illustrates an exemplary diagram of a network of oil processingplants in accordance with one or more embodiments of the presentinvention;

FIG. 3 illustrates an exemplary network representation of processingplants in accordance with one or more embodiments of the presentinvention;

FIG. 4 illustrates a flow diagram of a process for optimizing amanufacturing and process control system in accordance with one or moreembodiments of the present invention; and

FIG. 5 illustrates a block diagram of a computer system for use inimplementing one or more embodiments of the present invention.

The diagrams depicted herein are illustrative. There can be manyvariations to the diagrams or the operations described therein withoutdeparting from the spirit of the invention. For instance, the actionscan be performed in a differing order, or actions can be added, deleted,or modified. Also, the term “coupled” and variations thereof describeshaving a communications path between two elements and does not imply adirect connection between the elements with no interveningelements/connections between them. All of these variations areconsidered a part of the specification.

DETAILED DESCRIPTION

One or more embodiments of the present invention providecomputer-implemented methods, computing systems, and computer programproducts for optimizing a throughput production of each productionfacility of a network of production facilities.

Modern manufacturing and processing facilities are arranged as a networkof remote plants, in which each plant completes a step towardsconverting raw materials into marketable products. Each plant in thenetwork includes a self-contained set of inputs and outputs for each ofthe plant's sub-processes. The control systems use predictive models toguide the overall process by monitoring the relationship between variousset-points (controllable variable values), material inflows, andthroughput. For example, oil processing involves multiple remotefacilities that each perform separate functions include separatingresiduals from crude oil, converting the residuals into marketableproducts, and treating the marketable products to remove anycontaminants. The individual control systems use predictive models todetermine an expected throughput from each oil processing facility andregulate the facilities based on a comparison of actual throughput topredicted throughput.

To ensure that the control systems produce the maximum amount ofmarketable products, large-scale optimization measures are implementedinto the control systems. The large-scale optimization methods need toaccount for operational restrictions and non-linear relationshipsbetween inflows and outflows. Conventional optimization methods rely onindustry-specific models that are too costly to be portable to otherindustries or, in some instances, unavailable. In some instances,conventional optimization models, are either implicitly defined ordefine processes as a black box. As a result of poor portability andblack box approximations, the conventional optimization methods areunable to account for randomness in raw materials or unexpectedbreakdowns in a process.

One or more embodiments of the present invention address one or more ofthe above-described shortcomings by providing computer-implementedmethods, computing systems, and computer program products to optimizethe operation of a production plant of a multi-plant network. Theoptimization can be achieved by deriving optimal set-points and flowsfor an entire process, recasting the multi-plant network into asurrogate network of regression transformers that capture the essentialprocess input to output relationships at each plant. The representationis coupled with operational constraints to develop aprediction-optimization formulation plant-wide optimization.

Turning now to FIG. 1 , a manufacturing and process control system 100is generally shown in accordance with one or more embodiments of thepresent invention. The control system 100 is a computer-based systemthat regulates the operation of connected electrical and mechanicaldevices via the use of feed-forward or feedback control loops. Thecontrol system 100 is operable to detect a predictive model type used bya sub-control system of a plant and determine the optimal set valuesbased on the predictive model type. The control system 100 furthermonitors the inputs and outputs of the process performed at the plant,and adjusts the process based on not achieving the desired throughput.The control system 100 is in operable communication with a network ofsub-control systems, in which each sub-control system is an overallcontrol system of a processing plant of a network of processing plants.As illustrated, the control system 100 is in operable communication witha first sub-control system 102, a second sub-control system 104, and athird sub-control system 106. Each of the first, second, and thirdsub-control system 102 104 106 includes a respective fleet of sensors108 and at least one actuator 110. The actuator 110 is operable to moveor control a machine involved in at least one step of the processperformed at the processing plant Furthermore, at least one sensor ofthe fleet of sensors 108 is operable for sensing and collecting datafrom the actuator 110 and transmitting the data back to the controlsystem 100. It should be appreciated that although FIG. 1 illustratesthree sub-control systems 102 104 106, the control system 100 can be inoperable communication with any number of sub-control systems used tocontrol a network of processing plants.

The control system 100 is in operable communication with each respectivefirst, second, and third sub-control system 102 104 106 of eachprocessing plant of the network of processing plants. Each of the first,second, and third sub-control systems 102 104 106 applies a predictivemodel (e.g., a regression model) to calculate a predicted throughout atthe plant. For the purposes of explanation, the first sub-control system102 is discussed herein. However, this discussion applies to anysub-control system of the network of processing plants. The firstsub-control system 102 uses a predictive model, for example, aregression model to collect data from the processing plant and calculatethe optimal throughput. The control system 100 can detect the type ofpredictive model used by the first sub-control system 102 and determinewhether the predictive model is a linear-based predictive model or agradient-based model. The control system 100 can detect the type ofpredictive model based on accessing a processing plant network databaseand read the type of predictive model. The control system 100 can alsoaccess the first sub-control system 102 and extract characteristics ofthe predictive model and compare the characteristics to a dictionary ofpredictive models.

For each the sub-control system, a prediction model is used to learn therelationship between the control variables and the output. Whether thesub-control system is applying a linear predictive model or a non-linearpredictive model, the control system 100 can model the network ofprocessing plants as follows (the model is illustrated in further detailat FIG. 3 ). As shown in FIG. 3 , the plant is represented as ahierarchy structure with L layers having upstream-downstream operationrelations. FIG. 3 is a feed-forward network representation for theplant. A circular node in a layer of the network represents a plant(i.e., a sub-system), where a regression function is built. Arectangular node represents all operational constraints such asmaintaining inventory levels and limits on the adjustment of variablesfrom the preceding time period. The relationship in these rectangularnodes are often linear.

The predictive model ƒ_(l) can be a linear-based predictive model or ahighly non-linear-based predictive models, in which a gradient isavailable. The linear-based predictive model type can includelinear-based regression functions, decision trees, piece-wiselinear-based regression functions, gradient-boosted trees, multivariateadaptive regression splines (MARS), fully connected feed-forward network(FFN), and other similar models. The highly non-linear predictive model(gradient-based predictive model) can include deep neural networks(DNN), support vector machines (SVN), and other similar models.Regardless of the type of predictive model, the predictive model can bebuilt through machine learning and executed on a neural network. Thepredictive model can be trained using industry-specific historical data.

The plant consists of a consecutive network of processes (e.g.,sub-control systems), where processes at the l-th layer in FIG. 3 can bedescribed by the following vector-valued regression function:ƒ_(l):(z _(l−1) ,x _(l))∈

^(k) ^(l−1) ^(+m) ^(l) →y _(l)∈

^(n) ^(i)where x_(l)∈

^(m) ^(l) are the controllable variables (e.g., set-points) and z_(i−1)∈

^(k) ^(l−1) are the uncontrollable variable (e.g., the inflow from aprevious process or predecessor plant).

The vector y_(i)∈

^(nl) are the outflows from processes at the l-th layer. As describedabove, k₀=0; that is, the decision variables for the first layer areonly set-points. The control system 100 can find the optimal set-pointsxi and flow rates (y_(l), z_(l)) to maximize processing plant productionor some other target variable. The relationship between inputs and anoutput for an industrial plant is often complex, a non-linear predictionmodel should be used to capture the complexity rather than a linearmodel. A single-period model can be described as the nonconvexconstrained optimization problem below:

$\begin{matrix}{\min\limits_{X}{\sum\limits_{i = 1}^{L}{\phi_{l}( y_{l} )}}} & (1)\end{matrix}$ $\begin{matrix}{s.t.} & {{y_{1} = {f_{1}( x_{1} )}},}\end{matrix}$ y_(l) = f_(l)(z_(l − 1), x_(l)), ∀l = 2, …, L,A_(l)y_(l) + B_(l)z_(l) ≤ b_(l), ∀l = 1, …, L − 1,${{\underline{x}}_{l} \leq x_{l} \leq {\overset{\_}{x}}_{l}},{{\forall l} = 1},\ldots,L,$where X=(x_(l), . . . , x_(L); y_(L); z_(l), . . . , z_(L−1)), and theobjective function Σ_(l=1) ^(L)ϕ_(l)(y_(l)) depends on the outputs foreach process. Where x _(l) and x _(l) are upper and lower bounds oncontrol set-points. The regression model needs to be cognizant ofoperational domain constraints. Therefore, model parameter matricesA_(l), B_(l) and vector b_(l) are used to capture interactions betweennodes within two consecutive network layers (plants). One example foroperational constraints to be included in A_(lyl)+B_(lzl)≤b_(l) is thetank storage constraint for the fourth tank, T4, 214 (i.e., l=2), asseen in FIG. 2 :u ₂ −u ₂ ⁰ ≤y ₂ −z ₂ ¹ −z ₂ ² ≤ū ₂−₂ ⁰,  (2)where u₂ ⁰ is the initial storage level, u ₂ and ū₂ are the lower andupper limits for storage tank T4.

The second nonconvex program for multi-period planning horizon T beingdescribed as follows:

$\begin{matrix}{\min\limits_{X^{t},u_{l}^{t}}{\sum\limits_{t = 1}^{T}{\sum\limits_{l = 1}^{L}{\phi_{l}( y_{l}^{t} )}}}} & (3)\end{matrix}$ $\begin{matrix}{s.t.} & {( {1 - \alpha} )u_{l}^{t - 1}}\end{matrix} \leq u_{l}^{i} \leq {( {1 + \alpha} )u_{l}^{t - 1}}$(1 − β)x_(l)^(t − 1) ≤ x_(l)^(t) ≤ (1 + β)x_(l)^(t − 1)u_(l)^(t) = u_(l)^(−t − 1) + y_(l)^(t) − z_(l)^(t)${\underline{u}}_{l} \leq u_{l}^{t} \leq {\overset{\_}{u}}_{l}$X^(t) ∈ 𝓍^(t), (l = 1, …, L, t = 1, …, T),where x^(l) is the set of constraints for the t-the period having a formof (1), u _(l) and ū_(l) are tank storage limits. The parameters α,β∈[0,1] is used to limit the amount of adjustment for a set-point fromthe time period t to the period t+1. The initial operating points X⁰ andu⁰ at time t=0 are assumed to be fixed and given, possibly from thecurrent operation time.

Conventional non-linear optimization algorithms devoted to a nonconvexprogram cannot guarantee the generation of a global minimizer, and theypredict based on a local minimizer rather than a global minimizer. Insome industries such as the oil and gas industry, a small improvement tosolution techniques can have a significant economic impact; for example,a 5% increase in control efficiency can results in billions of dollarsof additional revenue for the oil and gas industry. The herein describedcomputer-implemented methods, computing systems, and computer programproducts utilize a mixed-integer linear program (MILP) to obtain aglobally optimal solution to the nonconvex (possibly nonsmooth) problemwithin a reasonable run time.

To solve optimization problems (1) and (3), the present disclosureclassifies the type of prediction functions into: piece-wise linearfunctions such as random forest and differentiable functions such asconvolutional neural networks. For piece-wise linear functions, theseproblems can be solved by using a mixed-integer linear program. Forgradient-based functions, these problems can be solved by using amixed-integer linear program can be solved by a nonlinear optimizationalgorithm.

For partition regressions based on piece-wise linear approach suchdecision trees, multivariate adaptive regression splines (MARS), anddecision lists, nonconvex programs formulate (for example, (1) and (3))are formulated as a respective mixed-integer linear program (MILP). Themixed-integer linear representation is used for each respectiveregression function ƒ_(l). As exemplary illustrations, a MILP model forthree models: Decision tree-based ensemble models, multivariate adaptiveregression splines (MARS), and feed-forward deep neural networks areshown.

A tree ensemble model combines predictions from multiple decision treesƒ_(t)(x). A decision tree uses a tree-like structure to predict theoutcome for an input feature vector x. The t-th regression tree in theensemble model has the following form:

$\begin{matrix}{{f_{t}(x)} = {\sum\limits_{i = 1}^{M_{t}}{( {{a_{t,i}^{T}x} + b_{t,i}} ) \cdot {I( {x \in R_{t,i}} )}}}} & (4)\end{matrix}$where R_(t,I), . . . , Rt, M_(t) represent a partition of feature space,and I is the indicator function. In practice, individual decision treesoften suffer from high variance predictions and can overfit the trainingdata, which lead to a poor out-of-sample predictive accuracy, if thereis no restriction in the size of tree. By using the bagging techniques,the tree ensemble regression function outputs predictions by taking theweighted sum of multiple decision trees as:

$\begin{matrix}{{{f(x)} = {\sum\limits_{t = 1}^{T}{\lambda_{t}{f_{t}(x)}}}},} & (5)\end{matrix}$where λ_(t) is the weight for the decision tree ƒ_(t)(x). Parametersa_(t,i), b_(t,i), R_(t,i) and λ_(t) have been learned from thehistorical data.

An individual decision tree regression y=ƒ_(t)(x) consists of leaf nodesL and branching nodes B. For each leaf node lϵL, a linear model of theform r_(l)(x)=w_(l) ^(T)+c_(l) has been learned from the training databased on the points assigned to the leaf node. A branching node lϵB isrepresented by a hyperplane a_(l) ^(T)x+b_(l), where if a_(l)^(T)x+b_(l)<0 then the point x will follow the left branch from thenode, otherwise it splits into the right branch. Since the topology ofthe tree is fixed, for each feature vector x, there is a unique pathleading to a leaf node lϵL from the root of the tree. Let N_(L)(l)denote the ancestor nodes of l where the left branch is followed on thepath from the root to l, and let N_(R)(l) denote the set of right branchancestors on the path. The binary variable e_(l)ϵ{0,1}, lϵL, indicatesif x is assigned to leaf node l then e_(l)=1. Exactly one leaf node isselected for a data point x, where

$\begin{matrix}{{\sum\limits_{\ell \in \mathcal{L}}e_{\ell}} = L} & (6)\end{matrix}$

To determine the unique path routing to a leaf node, with the help ofthe indicator variable e_(t), the following constraints are enforced formodeling the splitting at branching nodes:a _(k) ^(T) x+b _(k) ≤M ₁(1−e

)−ϵ,∀

∈

,k∈

_(L)(

)a _(k) ^(T) x+b _(k) ≥−M ₂(1−e

),∀

∈

,k∈

_(R)(

),  (7)Where M₁ and M₂ are big positive numbers, and a very small ϵ>0. Thedecision tree regression y=ƒ_(t)(x) can be represented as amixed-integer bi-linear model

$\begin{matrix}{{y = {\sum\limits_{\ell \in \mathcal{L}}{e_{\ell}( {{w_{\ell}^{T}x} + e_{\ell}} )}}},} & (8)\end{matrix}$The bi-linear term e_(l)(w_(l) ^(T)+c_(l)) can be reformulated to a setof linear equations. Assume y_(l) ^(L)≤w_(l) ^(T)+c_(l)≤y_(l) ^(U) forsome constants y_(l) ^(L) and y_(l) ^(U). Then y_(l)=e_(l)(w_(l)^(T)+c_(l)) is equivalent toy _(l) ^(L) e _(l) ≤y _(l) ≤y _(l) ^(U) e _(l)w _(l) ^(T) x+e _(l) −y _(l) ^(U)(1−e _(l))≤y _(l) ≤w _(l) ^(T) x+e _(l)−y _(l) ^(L)(1−e _(l)).  (9)

Based on the above, control system 100 uses the following mixed-integerlinear representation for a decision tree-based model regressiony=ƒ_(t)(x):

$\begin{matrix}{{f(x)} = {\sum\limits_{i = 1}^{T}{\lambda_{t}{\sum\limits_{\ell \in \mathcal{L}}{y}_{\ell}}}}} & (10)\end{matrix}$ $\begin{matrix}{s.t.} & {{\sum\limits_{\ell \in \mathcal{L}}e_{\ell}} = 1}\end{matrix}$a_(k)^(T)x + b_(k) ≤ M₁(1 − e_(ℓ)) − e, ∀ℓ ∈ ℒ, k ∈ 𝒩_(L)(ℓ)a_(k)^(T)x + b_(k) ≥ −M₂(1 − e_(ℓ)), ∀ℓ ∈ ℒ, k ∈ 𝒩_(R)(ℓ)y_(ℓ)^(L)e_(ℓ) ≤ y_(ℓ) ≤ y_(ℓ)^(U)e_(ℓ)w_(ℓ)^(T)x + e_(ℓ) − y_(ℓ)^(U)(1 − e_(ℓ)) ≤ y_(ℓ) ≤ w_(ℓ)^(T)x + e_(ℓ) − y_(ℓ)^(L)(1 − e_(ℓ))e_(ℓ) ∈ {0, 1}, ∀ℓ ∈ ℒ,

For a multivariate adaptive regression spline (MARS), the control unit100 considers the regression spine fitting of degree 1: h(x)=α₀+Σ_(i=1)^(N)α_(i)h_(i)(x), where α₁ are scalars and h_(i)(x)=max{w_(i)^(T)+c₁,0}. The control unit 100 applies the following linearrepresentation:

$\begin{matrix}{{h(x)} = {\alpha_{0} + {\sum\limits_{i = 1}^{N}{\alpha_{i}y_{i}}}}} & (11)\end{matrix}$ $\begin{matrix}{s.t.} & {{y_{i} \geq {{w_{i}^{T}x} + c_{i}}},{i = 1},\ldots,N}\end{matrix}$ y_(i) ≤ (w_(i)^(T)x + c_(i)) + M₃e_(i), i = 1, …, Ny_(i) ≤ M₄(1 − e_(i)), i = 1, …, Ne_(i) ∈ {0, 1}, y_(i) ≥ 0, i = 1, …, N,

For a feed-forward deep neural network (DNN), for example a rectifiedlinear unit (ReLU) deep neural network with K+1 layers. Indexed from 0to K, which is used to model a non-linear function ƒ(x):

^(n) ⁰ →

^(n) ^(K) with n_(K)=1. For each hidden layer 1≤k≤K−1, the output vectorx_(k) is computed as x_(k)=σ(W_(k)x_(k−1)+b_(k)), where σ is the ReLUfunction, W_(k)ϵ

^(n) ^(K) ^(×n) ^(k−1) , b_(k)ϵ

^(n) ^(K) . For each layer k, assume there exists L_(k), U_(k)ϵ

such that L_(k)e_(k)≤W_(k)x_(k−1)+b_(k)≤U_(k)e_(k), e_(k)=(1, . . . ,1)ϵ

^(n) ^(K) . Therefore, the MILP model for a deep neural network is:

$\begin{matrix}\begin{matrix}{{{x_{k} - s_{k}} = {{W_{k}x_{k - 1}} + b_{k}}},} & {{k = 1},\ldots,{K - 1}}\end{matrix} & (12)\end{matrix}$ $\begin{matrix}{x_{k},{s_{k} \geq 0},} & {{k = 1},\ldots,{K - 1}}\end{matrix}$ $\begin{matrix}{{z_{k} \in \{ {0,1} \}^{n_{k}}},} & {{k = 1},\ldots,{K - 1}}\end{matrix}$ $\begin{matrix}{{x_{k} \leq {U_{k}z_{k}}},} & {{k = 1},\ldots,{K - 1}}\end{matrix}$ $\begin{matrix}{{s_{k} \leq {{- L_{k}}( {1 - z_{k}} )}},} & {{k = 1},\ldots,{K - 1}}\end{matrix}$ y = f(x₀) = W_(K)x_(K − 1) + b_(K),where two new variables are introduced: s_(k)ϵ

₊ ^(n) ^(k) and z_(k)ϵ{0,1}^(n) ^(k) . The control unit 100 can use thesame approach to have a MILP representation for other RE-type activationfunctions, including Leaky ReLU and Parametric ReLU.

The control unit 100 can further utilize a model to determine whetheradditional materials are needed to be added or removed for a process.For a regression function in the form y=f(x), the i-th materialcommitment is as follows:x _(i)∈[l,u] or x _(i)=0  (13)For some upper bound u and some lower bound l. The condition can bemodeled as:

$\begin{matrix}{{l \star s} \leq x_{i} \leq {u \star s}} & (14)\end{matrix}$ t − u(1 − s) ≤ x_(i) ≤ t − l(1 − s) l ≤ t ≤ u s ∈ {0, 1}These equations can be added to a MLIP model. The control unit 100 canthen cause a physical material to be added or removed from a processbased on the solution.

The control unit 100 can further determine whether a process needs to beenabled or disabled. For a process commitment either y=ƒ(x) or y=0. Thecontrol unit 100 assumes that the capacity of a process when operatingis a≤ƒ(x)≤b. The following equations are then added to the model aplant's status:

$\begin{matrix}{{a \star v} \leq y \leq {b \star v}} & (15)\end{matrix}$ f(x) − b(1 − v) ≤ y ≤ f(x) − a(1 − v) a ≤ f(x) ≤ bv ∈ {0, 1}The control unit 100 can then solve for the MILP model to determinewhether a process should be enabled or disabled.

The control system 100 can solve for the set variable and flow variablebased on applying a mixed-integer linear program, when the predictivemodels are piece-wise linear functions such as random forest,multivariate adaptive regression splines and fully connectedfeed-forward network.

In the event that the sub-control system is applying a non-linearpredictive model, the control system 100 can apply the followingprimal-dual optimization algorithm. The control system 100 can solve theabove referenced model by a two-level augmented Lagrangian method whengradients of ƒ_(l) are available. The control system 100 can treatnon-linear local constraints y_(l)=ƒ_(l)(⋅) and the linear couplingconstraints A_(lyl)+B_(lzl)≤b_(l) differently. The control system 100applies an augmented Lagrangian method to non-linear couplingconstraints in the outer loop. The control system 100 applies amulti-block alternating direction method of multipliers (ADMM) to thelinear coupling constraints at the inner level.

In order to apply a multi-block ADMM to a single period-model, thecontrol system 100 adds a slack variable u_(l) for the linearconstraint, such thatA _(lyl) +B _(lzl) +v _(l) −b _(l) +u _(l)=0; and u _(l)=0.  (16)The control system 100 then solves the optimization problem using anaugmented Lagrangian method with both constraints, y_(l)=ƒ_(l)(⋅) andu_(l)=0 by the following algorithm. First, the control unit 100 canconsider the following subproblem in the augmented Lagrangian method

$\begin{matrix}{{\min F( {\hat{u},\hat{v},\hat{x},\hat{y},\hat{z},{\hat{\lambda}}^{k},{{\hat{v}}^{k};\beta^{k}},\gamma^{k}} )} = {{\phi( y_{L} )} + {( \lambda_{1}^{k} )^{T}( {y_{1} - {f_{1}( x_{1} )}} )} + {\frac{\beta^{k}}{2}{{y_{1} - {f_{1}( x_{1} )}}}^{2}} + {\sum\limits_{l = 2}^{L}{( \lambda_{l}^{k} )^{T}( {y_{l} - {f_{l}( {z_{l - 1},x_{l}} )}} )}} + {\frac{\beta^{k}}{2}{\sum\limits_{l = 2}^{L}{{y_{l} - { {f_{l}( {z_{l - 1},x_{l}} )} )^{2}} + {\sum\limits_{l = 1}^{L - 1}{( v_{l}^{k} )^{T}u_{l}}} + {\frac{\gamma^{k}}{2}{\sum\limits_{l = 1}^{L - 1}{u_{l}}^{2}}}}}}}}} & (17)\end{matrix}$ $\begin{matrix}{{{{{s.t.{}A_{l}}y_{l}} + {B_{l}z_{l}} + v_{l} - b_{l} + u_{l}} = 0},} & {{{\forall l} = 1},\ldots,{L - 1},}\end{matrix}$${{\underline{x}}_{l} \leq x_{l} \leq {\overset{\_}{x}}_{l}},{{\underline{y}}_{l} \leq y_{l} \leq {\overset{\_}{y}}_{l}},{{\forall l} = 1},\ldots,L,$${{\underline{z}}_{l} \leq z_{l} \leq {\overset{\_}{z}}_{l}},{v_{l} \geq 0},{{\forall l} = 1},\ldots,{L - 1.}$The augmented Lagrangian method is provided below where h({circumflexover (x)}, ŷ, {circumflex over (z)})=[y₁−ƒ₁(y₁), y₂−ƒ₂(z₁, y₂), . . .y_(l)−ƒ_(L)(z_(L−1),y_(L))].

ALGORITHM 1: Two-level ALM 1: Initialize starting points (û⁰,{circumflexover (v)}⁰,{circumflex over (x)}⁰,ŷ⁰,{circumflex over (z)}⁰); β¹, γ¹ >0, ω ∈ (0, 1), r > 1; index k ← 1; 2: while some stopping criterion isnot satisfed do 3:  /* Inner level problem */ 4:  Solve (20) by amulti-block ADMM to get  (û^(k),{circumflex over (v)}^(k),{circumflexover (x)}^(k) ŷ^(k),{circumflex over (z)}^(k),μ^(k)) for ({circumflexover (λ)}^(k),β^(k)) and ({circumflex over (v)}^(k),γ^(k)); 5:  if∥h({circumflex over (x)}^(k),ŷ^(k),{circumflex over (z)}^(k))∥ ≤ω∥h({circumflex over (x)}^(k − 1),ŷ^(k −1),{circumflex over(z)}^(k −1))∥ then 6:   {circumflex over (λ)}^(k +) ¹ ← {circumflex over(λ)}^(k) + β^(k)h({circumflex over (x)}^(k), ŷ^(k), {circumflex over(z)}^(k)), β^(k +) ¹ ← β^(k); 7:  else 8:   {circumflex over (λ)}^(k +)¹ ← {circumflex over (λ)}^(k), β^(k +) ¹ ← rβ^(k); 9:  end if 10:  if∥û^(k)∥ ≤ ω∥ū^(k −) ¹∥ then 11:   {circumflex over (v)}^(k + 1) ←{circumflex over (v)}^(k) + γ^(k) û^(k), γ^(k + 1) ← γ^(k); 12:  else13:   {circumflex over (v)}^(k + 1) ← {circumflex over (v)}^(k),γ^(k + 1) ← rγ^(k); 14:  end if 15:  k ← k − 1; 16: end while (18)

The theoretical convergence results for the two-level augmentedLagrangian method when combining with a multi-block ADMM can be seen asfollows. The first assumption is that F(û,{circumflex over(v)},{circumflex over (x)},ŷ,{circumflex over (z)},{circumflex over(λ)}^(k),{circumflex over (v)}^(k),{circumflex over (β)}^(k),{circumflexover (γ)}^(k)) is continuously differentiable. The second assumption isthat the inner level ADMM outputs an approximate solution {(û^(k),v^(k), {circumflex over (x)}^(k),ŷ^(k),{circumflex over (z)}^(k),û^(k))to the following conditions

$\begin{matrix}{{d_{1}^{k} \in {{\nabla{f( {{\hat{x}}^{k},{\hat{y}}^{k},{\hat{z}}^{k}} )}} + {{\nabla{h( {{\hat{x}}^{k},{\hat{y}}^{k},{\hat{z}}^{k}} )}^{T}}( {{\overset{\_}{\lambda}}^{k} + {\beta^{k}{h( {{\hat{x}}^{k},{\hat{y}}^{k},{\hat{z}}^{k}} )}}} )} + {N_{\mathcal{X}}( {{\hat{x}}^{k},{\hat{y}}^{k},{\hat{z}}^{k}} )} + {C^{T}\mu^{k}}}},{d_{2}^{k} \in {\mu^{k} + {N_{\hat{\mathcal{X}}}( {\hat{v}}^{k} )}}},{{{A{\hat{y}}^{k}} + {B{\hat{z}}^{k}} + {\hat{v}}^{k} - b + {\hat{u}}^{k}} = d_{3}^{k}},{{{\hat{v}}^{k} + {\gamma^{k}{\hat{u}}^{k}} + \mu^{k}} = 0},} & (19)\end{matrix}$Wherelim_(k→∞) ∥d _(i) ^(k)∥=0 for i=1,2,3,ƒ({circumflex over(x)},ŷ,{circumflex over (z)})=φ(y _(L))  (20)Also where C=[0 A B], which is a matrix associated with ({circumflexover (x)}, ŷ, {circumflex over (z)}) in the linear constraint. X and Xare the box constraints for ({circumflex over (x)}, ŷ, {circumflex over(z)}) and {circumflex over (v)}, respectively.

For the last block of inner level ADMM, the linear constraint related toû is an identity matrix and the objective function is a convex andquadratic function. Under mild conditions on the functions f, h and thematrices A, B, the multi-block ADMM algorithm can converge(subsequently) to a stationary point of the subproblem (17) andtherefore the second Assumption can be satisfied.

The multi-period formulation (3) can be compactly expressed as follows:

$\begin{matrix}{\min\limits_{w^{1},\ldots,w^{T}}{\sum\limits_{t = 1}^{T}{\phi^{i}( w^{t} )}}} & (21)\end{matrix}$ $\begin{matrix}{s.t.} & {{w^{l} \in \Omega^{t}},{t = 1},\ldots,T}\end{matrix}$ M^(t − 1)w^(t − 1) + N^(t)w^(t) + c^(t) = 0,where w=(X, u, p, q, r, s) and the constraint set Ω^(t) is related toX^(t), bounds for u, and positivity constraints for p, q, r, and s. Theparameters M^(t), N^(t), and c^(t) are determined from the couplingconstraints.

The phrases “neural network” and “machine learning” broadly describes afunction of electronic systems that learn from data. A machine learningsystem, engine, or module can include a machine learning algorithm thatcan be trained, such as in an external cloud environment (e.g., a cloudcomputing environment), to learn functional relations between inputs andoutputs that are currently unknown. In one or more embodiments, machinelearning functionality can be implemented using a predictive model,having the capability to be trained to perform a currently unknownfunction. In machine learning and cognitive science, neural networks area family of statistical learning models inspired by the biologicalneural networks of animals, and in particular, the brain. Neuralnetworks can be used to estimate or approximate systems and functionsthat depend on a large number of inputs.

The predictive model can be embodied as so-called “neuromorphic” systemsof interconnected processor elements that act as simulated “neurons” andexchange “messages” between each other in the form of electronicsignals. Similar to the so-called “plasticity” of synapticneurotransmitter connections that carry messages between biologicalneurons, the connections in the predictive model that carry electronicmessages between simulated neurons are provided with numeric weightsthat correspond to the strength or weakness of a given connection.During training, the weights can be adjusted and tuned based onexperience, making the control system 100 adaptive to inputs and capableof learning. After being weighted and transformed by a functiondetermined by the network's designer, the activation of these inputneurons are then passed to other downstream neurons, which are oftenreferred to as “hidden” neurons. This process is repeated until anoutput neuron is activated. The activated output neuron determines whichcharacter was read.

Referring to FIG. 2 , an exemplary diagram 200 of a network of oilprocessing plants in accordance with one or more embodiments of thepresent invention is shown. In connection with FIG. 2 , optimization caninvolve devising production strategies that maximize synthetic crude oil(SCO) production, under both normal operations as well as unplannedupsets and breakdowns. Starting with mined oil sands, the first step isto extract bitumen as froth and store it in a storage tank. The firstplant, P1, 202 and the second plant, P2, 202 are two parallel froth anddiluted bitumen production plants. The first tank, T1, 206 and thesecond tank, T2, 208 are intermediate storage tanks. The third tank, T3,210 stores diluted bitumen. The diluted bitumen is passed through anupgrading third plant, P3, 212, to produce low-quality SCO that getsstored in a fourth tank, T5, 214. This is an intermediate product thatis either sold directly to refineries or is further processed in afourth plant, P5, 216 and a fifth plant, P6, 218 that are parallelupgraders that produce different grades of synthetic crude oil.

Each of the first, second, third, fourth, and fifth plants 202, 204,212, 216, 218 are controlled by a sub-control system. Each sub-controlsystem employs a respective predictive model to calculate predictedthroughputs at each respective plant. The predictive models can each bea same type of predictive model or at least one of the first, second,third, fourth, and fifth plants 202, 204, 212, 216, 218 can employ adifferent type of predictive model.

Referring to FIG. 3 , an exemplary network representation 300 ofprocessing plants described in FIG. 2 in accordance with one or moreembodiments of the present invention is shown. The representation 300 isviewed as a hierarchal structure with L layers havingupstream-downstream operation relations. The first node 302, second node304, third node 306, fourth node 308, and fifth node 310 represent arespective plant (i.e., a sub-system) from FIG. 2 , where a predictivemodel is built. The first rectangular node 312 and the secondrectangular node 314 represents all the operational constraints, such asmaintaining inventory levels and limits on the adjustment of variablesfrom the preceding time period. The relationship in these rectangularnodes 312 314 are often linear. In some embodiments of the presentinvention, these rectangular nodes 312 314 represent a volume of fluidin one or more storage tanks. It should be appreciated that FIGS. 2 and3 only illustrate one particular arrangement of a network of plants,however, the herein described computer-implemented methods, computingsystems, and computer programs products are applicable to any number ofnetwork arrangements.

Referring to FIG. 4 , a computer-implemented process 400 for optimizinga manufacturing and process control system in accordance with one ormore embodiments of the present invention is shown. In accordance withembodiments of the invention, the process 400 is implemented by thecontrol system 100. At block 402, the control system 100 determines atype of predictive model used by a sub-control system of a plant of anetwork of plants. The network of plants being arranged for the purposesof completing separate processing stages of one or more products. Thepredictive model can be a linear-based predictive model or anon-linear-based predictive model. The control system 100 can determinethe type of predictive model by accessing the sub-control system andanalyzing the predictive model. The control system 100 can also access anetwork database with a description of each predictive model used ateach plant of a network of plants.

At block 404, the control system 100 selects an optimization algorithmbased on the type of predictive model used by the sub-control system ofthe plant. Regardless of type of predictive model, the control system100 used the selected optimization algorithm to solve a model of theplant to determine optimal set variables and outflow values at theplant. In the event that the plant uses a linear-based predictive model,the control system 100 uses a mixed-integer linear program to solve forthe optimization. If the plant uses a non-linear-based predictive model,the control system takes into account both linear and non-linearconstraints and solves the optimization through an augmented Lagrangianmethod.

At block 406, the control system 100 solves for the optimum values forthe set-points and outflow values. As described above, the controlsystem 100 uses a mixed-integer linear program to solve for theoptimization of a linear model. Alternatively, the control system 100uses an augmented Lagrangian method to solve the optimization of anon-linear predictive model.

At block 408, the control system 100 applies the optimum set-points andoutflow values to determine and optimum throughput value for the plant.The control system 100 further receives actual throughput values fromsensors arranged on or about the plant. The sensor values can include avolume, quality, or time of processing of fluid processed by the plant.The control system 100 further compares the measured throughput to thepredicted throughput.

At block 410, the control system 100 determines whether the measuredthroughput values are within a threshold value of the predictedthreshold value. The threshold value can include an upper bound and alower bound. The control system 100 can further determine whether themeasured value is within the upper bound and the lower bound. At block412, if the measured value is within the upper bound and the lowerbound, the control system 100 takes no further action. However, if themeasured value is not within the upper bound and lower bound, thecontrol system 100 can suspend one or more processes at the plant. Thecontrol system 100 can cause an actuator at the plant to cease tofunction, thereby suspending the process.

It is understood that the present disclosure is capable of beingimplemented in conjunction with any other type of computing environmentnow known or later developed. For example, FIG. 5 depicts a blockdiagram of a processing system 500 for implementing the techniquesdescribed herein. In examples, the processing system 500 has one or morecentral processing units (processors) 521 a, 521 b, 521 c, etc.(collectively or generically referred to as processor(s) 521 and/or asprocessing device(s)). In aspects of the present disclosure, eachprocessor 521 can include a reduced instruction set computer (RISC)microprocessor. Processors 521 are coupled to system memory (e.g.,random access memory (RAM) 524) and various other components via asystem bus 533. Read only memory (ROM) 522 is coupled to system bus 533and may include a basic input/output system (BIOS), which controlscertain basic functions of the processing system 500.

Further depicted are an input/output (I/O) adapter 527 and a networkadapter 526 coupled to the system bus 533. I/O adapter 527 may be asmall computer system interface (SCSI) adapter that communicates with ahard disk 523 and/or a storage device 525 or any other similarcomponent. I/O adapter 527, hard disk 523, and storage device 525 arecollectively referred to herein as mass storage 534. Operating system540 for execution on processing system 500 may be stored in mass storage534. The network adapter 526 interconnects system bus 533 with anoutside network 536 enabling processing system 500 to communicate withother such systems.

A display (e.g., a display monitor) 535 is connected to the system bus533 by display adapter 532, which may include a graphics adapter toimprove the performance of graphics intensive applications and a videocontrol. In one aspect of the present disclosure, adapters 526, 527,and/or 532 may be connected to one or more I/O busses that are connectedto the system bus 533 via an intermediate bus bridge (not shown).Suitable I/O buses for connecting peripheral devices such as hard diskcontrols, network adapters, and graphics adapters typically includecommon protocols, such as the Peripheral Component Interconnect (PCI).Additional input/output devices are shown as connected to system bus 533via user interface adapter 528 and display adapter 532. An input device529 (e.g., a keyboard, a microphone, a touchscreen, etc.), an inputpointer 530 (e.g., a mouse, trackpad, touchscreen, etc.), and/or aspeaker 531 may be interconnected to system bus 533 via user interfaceadapter 528, which may include, for example, a Super I/O chipintegrating multiple device adapters into a single integrated circuit.

In some aspects of the present disclosure, the processing system 500includes a graphics processing unit 537. Graphics processing unit 537 isa specialized electronic circuit designed to manipulate and alter memoryto accelerate the creation of images in a frame buffer intended foroutput to a display. In general, graphics processing unit 537 is veryefficient at manipulating computer graphics and image processing and hasa highly parallel structure that makes it more effective thangeneral-purpose CPUs for algorithms where processing of large blocks ofdata is done in parallel.

Thus, as configured herein, the processing system 500 includesprocessing capability in the form of processors 521, storage capabilityincluding system memory (e.g., RAM 524), and mass storage 534, inputmeans such as keyboard 529 and mouse 530, and output capabilityincluding speaker 531 and display 535. In some aspects of the presentdisclosure, a portion of system memory (e.g., RAM 724) and mass storage534 collectively store the operating system 540 to coordinate thefunctions of the various components shown in the processing system 500.

Various embodiments of the invention are described herein with referenceto the related drawings. Alternative embodiments of the invention can bedevised without departing from the scope of this invention. Variousconnections and positional relationships (e.g., over, below, adjacent,etc.) are set forth between elements in the following description and inthe drawings. These connections and/or positional relationships, unlessspecified otherwise, can be direct or indirect, and the presentinvention is not intended to be limiting in this respect. Accordingly, acoupling of entities can refer to either a direct or an indirectcoupling, and a positional relationship between entities can be a director indirect positional relationship. Moreover, the various tasks andprocess steps described herein can be incorporated into a morecomprehensive procedure or process having additional steps orfunctionality not described in detail herein.

One or more of the methods described herein can be implemented with anyor a combination of the following technologies, which are each wellknown in the art: a discrete logic circuit(s) having logic gates forimplementing logic functions upon data signals, an application specificintegrated circuit (ASIC) having appropriate combinational logic gates,a programmable gate array(s) (PGA), a field programmable gate array(FPGA), etc.

For the sake of brevity, conventional techniques related to making andusing aspects of the invention may or may not be described in detailherein. In particular, various aspects of computing systems and specificcomputer programs to implement the various technical features describedherein are well known. Accordingly, in the interest of brevity, manyconventional implementation details are only mentioned briefly herein orare omitted entirely without providing the well-known system and/orprocess details.

In some embodiments, various functions or acts can take place at a givenlocation and/or in connection with the operation of one or moreapparatuses or systems. In some embodiments, a portion of a givenfunction or act can be performed at a first device or location, and theremainder of the function or act can be performed at one or moreadditional devices or locations.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting. As used herein, thesingular forms “a”, “an” and “the” are intended to include the pluralforms as well, unless the context clearly indicates otherwise. It willbe further understood that the terms “comprises” and/or “comprising,”when used in this specification, specify the presence of statedfeatures, integers, steps, operations, elements, and/or components, butdo not preclude the presence or addition of one or more other features,integers, steps, operations, element components, and/or groups thereof.

The corresponding structures, materials, acts, and equivalents of allmeans or step plus function elements in the claims below are intended toinclude any structure, material, or act for performing the function incombination with other claimed elements as specifically claimed. Thepresent disclosure has been presented for purposes of illustration anddescription, but is not intended to be exhaustive or limited to the formdisclosed. Many modifications and variations will be apparent to thoseof ordinary skill in the art without departing from the scope and spiritof the disclosure. The embodiments were chosen and described in order tobest explain the principles of the disclosure and the practicalapplication, and to enable others of ordinary skill in the art tounderstand the disclosure for various embodiments with variousmodifications as are suited to the particular use contemplated.

The diagrams depicted herein are illustrative. There can be manyvariations to the diagram or the steps (or operations) described thereinwithout departing from the spirit of the disclosure. For instance, theactions can be performed in a differing order or actions can be added,deleted or modified. Also, the term “coupled” describes having a signalpath between two elements and does not imply a direct connection betweenthe elements with no intervening elements/connections therebetween. Allof these variations are considered a part of the present disclosure.

The following definitions and abbreviations are to be used for theinterpretation of the claims and the specification. As used herein, theterms “comprises,” “comprising,” “includes,” “including,” “has,”“having,” “contains” or “containing,” or any other variation thereof,are intended to cover a non-exclusive inclusion. For example, acomposition, a mixture, process, method, article, or apparatus thatcomprises a list of elements is not necessarily limited to only thoseelements but can include other elements not expressly listed or inherentto such composition, mixture, process, method, article, or apparatus.

Additionally, the term “exemplary” is used herein to mean “serving as anexample, instance or illustration.” Any embodiment or design describedherein as “exemplary” is not necessarily to be construed as preferred oradvantageous over other embodiments or designs. The terms “at least one”and “one or more” are understood to include any integer number greaterthan or equal to one, i.e. one, two, three, four, etc. The terms “aplurality” are understood to include any integer number greater than orequal to two, i.e. two, three, four, five, etc. The term “connection”can include both an indirect “connection” and a direct “connection.”

The terms “about,” “substantially,” “approximately,” and variationsthereof, are intended to include the degree of error associated withmeasurement of the particular quantity based upon the equipmentavailable at the time of filing the application. For example, “about”can include a range of ±8% or 5%, or 2% of a given value.

The present invention may be a system, a method, and/or a computerprogram product at any possible technical detail level of integration.The computer program product may include a computer readable storagemedium (or media) having computer readable program instructions thereonfor causing a processor to carry out aspects of the present invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, configuration data for integrated circuitry, oreither source code or object code written in any combination of one ormore programming languages, including an object oriented programminglanguage such as Smalltalk, C++, or the like, and procedural programminglanguages, such as the “C” programming language or similar programminglanguages. The computer readable program instructions may executeentirely on the user's computer, partly on the user's computer, as astand-alone software package, partly on the user's computer and partlyon a remote computer or entirely on the remote computer or server. Inthe latter scenario, the remote computer may be connected to the user'scomputer through any type of network, including a local area network(LAN) or a wide area network (WAN), or the connection may be made to anexternal computer (for example, through the Internet using an InternetService Provider). In some embodiments, electronic circuitry including,for example, programmable logic circuitry, field-programmable gatearrays (FPGA), or programmable logic arrays (PLA) may execute thecomputer readable program instruction by utilizing state information ofthe computer readable program instructions to personalize the electroniccircuitry, in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the blocks may occur out of theorder noted in the Figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdescribed herein.

What is claimed is:
 1. A computer-implemented method comprising:applying, by a processor, an optimization algorithm to a control systemof a processing plant based on whether the control system is guided by alinear-based predictive model or a non-linear-based predictive model inwhich a gradient is available, wherein applying the optimizationalgorithm comprises: responsive to the control system being guided by alinear-based predictive model, applying a mixed-integer linear programto the linear-based predictive model, wherein the mixed-integer linearprogram comprises one or more individual decision trees, wherein atopology of each decision tree is fixed such that, for each featurevector x in the respective decision tree, there is a unique path leadingto a leaf node of the tree from the root of the tree; and responsive tothe control system being guided by a non-linear-based predictive model,applying a two-level augmented Lagrangian method to the non-linear-basedpredictive model, wherein an augmented Lagrangian method is applied tonon-linear coupling constraints in an outer level of the two-levelaugmented Lagrangian method and a multi-block alternating directionmethod of multipliers (ADMM) is applied to linear coupling constraintsin an inner level of the two-level augmented Lagrangian method;calculating, by the processor, a set variable using the optimizationalgorithm; predicting, by the processor, an output based on thecalculated set variable; comparing, by the processor, an actual outputat the processing plant to the predicted output; and suspending, by theprocessor, a physical process at the processing plant in response to theactual output being a threshold value apart from the predicted output.2. The computer-implemented method of claim 1, wherein calculation ofthe set variable is based at least in part on a measured volume of fluidprocessed by a predecessor processing plant.
 3. The computer-implementedmethod of claim 1, wherein the suspending a physical process comprisesdisabling an actuator.
 4. The computer-implemented method of claim 1,wherein the non-linear based model includes a deep neural network (DNN).5. The computer-implemented method of claim 1, wherein the processingplant is member of a network of processing plants.
 6. A systemcomprising: a memory having computer readable instructions; and one ormore processors configured to execute the computer readableinstructions, the computer readable instructions configured to controlthe one or more processors to perform operations comprising: applying anoptimization algorithm to a control system of a processing plant basedon whether the control system is guided by a linear-based predictivemodel or a non-linear-based predictive model in which a gradient isavailable, wherein applying the optimization algorithm comprises:responsive to the control system being guided by a linear-basedpredictive model, applying a mixed-integer linear program to thelinear-based predictive model, wherein the mixed-integer linear programcomprises one or more individual decision trees, wherein a topology ofeach decision tree is fixed such that, for each feature vector x in therespective decision tree, there is a unique path leading to a leaf nodeof the tree from the root of the tree; and responsive to the controlsystem being guided by a non-linear-based predictive model, applying atwo-level augmented Lagrangian method to the non-linear-based predictivemodel, wherein an augmented Lagrangian method is applied to non-linearcoupling constraints in an outer level of the two-level augmentedLagrangian method and a multi-block alternating direction method ofmultipliers (ADMM) is applied to linear coupling constraints in an innerlevel of the two-level augmented Lagrangian method; calculating a setvariable using the optimization algorithm; predicting an output based onthe calculated set variable; comparing an actual output at theprocessing plant to the predicted output; and suspending a physicalprocess at the processing plant in response to the actual output being athreshold value apart from the predicted output.
 7. The system of claim6, wherein calculation of the set variable is based at least in part ona measured volume of fluid processed by a predecessor processing plant.8. The system of claim 6, wherein the suspending a physical processcomprises disabling an actuator.
 9. The system of claim 6, wherein thenon-linear based model includes a deep neural network (DNN).
 10. Thesystem of claim 6, wherein the processing plant is member of a networkof processing plants.
 11. A non-transitory computer program productcomprising a computer readable storage medium having programinstructions embodied therewith, the program instructions executable bya processor to cause the processor to perform operations comprising:applying an optimization algorithm to a control system of a processingplant based on whether the control system is guided by a linear-basedpredictive model or a non-linear-based predictive model in which agradient is available, wherein applying the optimization algorithmcomprises: responsive to the control system being guided by alinear-based predictive model, applying a mixed-integer linear programto the linear-based predictive model, wherein the mixed-integer linearprogram comprises one or more individual decision trees, wherein atopology of each decision tree is fixed such that, for each featurevector x in the respective decision tree, there is a unique path leadingto a leaf node of the tree from the root of the tree; and responsive tothe control system being guided by a non-linear-based predictive model,applying a two-level augmented Lagrangian method to the non-linear-basedpredictive model, wherein an augmented Lagrangian method is applied tonon-linear coupling constraints in an outer level of the two-levelaugmented Lagrangian method and a multi-block alternating directionmethod of multipliers (ADMM) is applied to linear coupling constraintsin an inner level of the two-level augmented Lagrangian method;calculating a set variable using the optimization algorithm; predictingan output based on the calculated set variable; comparing an actualoutput at the processing plant to the predicted output; and suspending aphysical process at the processing plant in response to the actualoutput being a threshold value apart from the predicted output.
 12. Thecomputer program product of claim 11, wherein calculation of the setvariable is based at least in part on a measured volume of fluidprocessed by a predecessor processing plant.
 13. The computer programproduct of claim 11, wherein the suspending a physical process comprisesdisabling an actuator.
 14. The computer program product of claim 11,wherein the non-linear based model includes a deep neural network (DNN).